I'm having Abstract Algebra course in school this semester, and since the course is in English but my teacher explain it in Mandarin, it is very hard to memorize everything and link different things together. Your videos really helped :)
My abstract algebra teacher’s favorite line is “the notation is the reality” Big explanations have little explanations upon their back to bite them and little explanations have lesser explanations and so on infinitum. A. Rivera would love your comments on well defined functions!
Cool thing about this one is it helps tell you how to create homomorphisms since the diagram commutes, so any homomorphism between G and G’ has to be a composition of the isomorphism of the quotient group to G’ and an onto homomorphism from G to its quotient group.
Hello, what's the name of the previous video where you proved Ker(Phi) was a normal subgroup of G? Thanks a lot for all these videos, they are really helpful
Hi Prof Penn. .thanks for the insightful videos! .U indicated that u have a video with alot of applications of the first isomorphism theorem. .but I cannot see it..could you be so kind as to direct me..thanks!
Question: when you prove the isomorphism is unique, it is assuming the homomorphism mapping Pi is fixed. If Pi is defined in another way, called it Pi-hat, then the isomorphism Psi-bar need be changed according to the Pi-hat, right? so it will become Psi ( Pi (x) ) = Phi(x)= Psi-bar ( Pi-hat (x) ). Here the two isomorphism Psi and Psi-bar will be different.
@@elements-24 I don't know if you are still looking for an answer, but phi is any homomorphism, and pi is onto (pi(x) = x ker phi). If phi is onto, then we have G/ker phi is isomorphic to H.
Say "homomorphism psi" five times fast 😁
Awesome video series.
I'm having Abstract Algebra course in school this semester, and since the course is in English but my teacher explain it in Mandarin, it is very hard to memorize everything and link different things together. Your videos really helped :)
My abstract algebra teacher’s favorite line is “the notation is the reality”
Big explanations have little explanations upon their back to bite them and little explanations have lesser explanations and so on infinitum.
A. Rivera would love your comments on well defined functions!
Love this video- very clear and straight to the point…
This is incredible! Thanks so much for making these videos on isomorphism theorems, they help a lot!
Send love from Korea. I appreciate for your nice and kind classes. That is so helpful to me!
Cool thing about this one is it helps tell you how to create homomorphisms since the diagram commutes, so any homomorphism between G and G’ has to be a composition of the isomorphism of the quotient group to G’ and an onto homomorphism from G to its quotient group.
Thanks dude u cleared my concepts
10/10 explanation. thank you.
Hello, what's the name of the previous video where you proved Ker(Phi) was a normal subgroup of G? Thanks a lot for all these videos, they are really helpful
Such a beautiful theorem I love this
Thank u, so helpful 🌸💕
Thank you sir💙🙏
Hi Prof Penn. .thanks for the insightful videos! .U indicated that u have a video with alot of applications of the first isomorphism theorem. .but I cannot see it..could you be so kind as to direct me..thanks!
Here you go: th-cam.com/video/BE8lhcGfSiI/w-d-xo.html
It is over an hour of first isomorphism theorem examples!!
Hi can you also explain the isomorphism theorems for vector spaces?
Excellent
Question: when you prove the isomorphism is unique, it is assuming the homomorphism mapping Pi is fixed. If Pi is defined in another way, called it Pi-hat, then the isomorphism Psi-bar need be changed according to the Pi-hat, right? so it will become Psi ( Pi (x) ) = Phi(x)= Psi-bar ( Pi-hat (x) ). Here the two isomorphism Psi and Psi-bar will be different.
I work in AI for a long time and I use your videos to teach math to my daughters ... frankly what you are doing is just exceptional
9:25 had me wheezing ahaha
xKer(phi)=yKer(phi) means xy^-1 is in Ker(phi) but it should be that x^-1y is in Ker(phi)
Yea that confused me for a minute.
Came for exam revision stayed for the subtle dune merch.
Nice catch, I didn't notice the reference until now.
Could you please share your group theory playlist!
Thanks
One more question, do the maps phi and pi have to be onto homomorphism or just homomorphism?
@@elements-24 I don't know if you are still looking for an answer, but phi is any homomorphism, and pi is onto (pi(x) = x ker phi). If phi is onto, then we have G/ker phi is isomorphic to H.
10:20 from what you get this last equation ? xkerfi = ekerfi?
From what I understand, it follows directly from x being an element of ker(phi). Ker(phi) is a subgroup containing x, and so xker(phi) = ker(phi).
There is a proof in proof wili in the lemma left coset is equal to subgroup!